This work shows that the theoretical stress concentration factor depends on the length of the member in addition to the established other standard geometric parameters. In particular, the in-plane theoretical stress concentration factors for short rectangular plates with centered circular holes subjected to uniform tension are determined using the finite element method. It is shown that these factors can reach significantly larger values than the corresponding existing ones for long plates. The value of the transition length between long and short plates is computed and reported as well. Two new concepts are defined, short members and transition length.

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The values of the theoretical stress concentration factors for a variety of geometries and loads are available in a number of well-known publications. It is shown in this work that the reported existing results neglect the length of the members in the direction of the applied loads, and it is also shown that shorter lengths may have very significant effects on the magnitudes of the stress concentration factors. The finite element determined in-plane theoretical stress concentration factors for uniform thickness short shouldered plates subjected to uniform tension at the wide end and held longitudinally at the narrow end, for practical ranges of the fillet radius values, are reported and are presented in the standard graphical form. For completeness, other types of boundary condition have also been examined in this work. The value of the transition length between long and short plates is reported as well.

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A model for predicting temperature evolution for automatic controling systems in manufacturing processes requiring the coiling of bars in the transfer table is presented. Although the method is of a general nature, the presentation in this work refers to the manufacturing of steel plates in hot rolling mills. The predicting strategy is based on a mathematical model of the evolution of temperature in a coiling and uncoiling bar and is presented in the form of a parabolic partial differential equation for a shape changing domain. The mathematical model is solved numerically by a space discretization via geometrically adaptive finite elements which accomodate the change in shape of the domain, using a computationally novel treatment of the resulting thermal contact problem due to coiling. Time is discretized according to a Crank-Nicolson scheme. Since the actual physical process takes less time than the time required by the process controlling computer to solve the full mathematical model, a special predictive device was developed, in the form of a set of least squares polynomials, based on the off-line numerical solution of the mathematical model